Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling

We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$, the relative frequencies of sets $C\in\mathcal{C}$ converge uniformly to their limiting probabilities. Beyond ergodicity, no assumptions are imposed on the sampling process, and no regularity conditions are imposed on the elements of $\mathcal{C}$. The result extends existing work of Vapnik and Chervonenkis, among others, who have studied uniform convergence for i.i.d. and strongly mixing processes. Our method of proof is new and direct: it does not rely on symmetrization techniques, probability inequalities or mixing conditions. The uniform convergence of relative frequencies for VC-major and VC-graph classes of functions under ergodic sampling is established as a corollary of the basic result for sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOP511 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Kontribusi USAhatani Madu Sialang terhadap Pendapatan Keluarga Petani (Studi Kasus di Desa Gunung Sahilan Kecamatan Gunung Sahilan Kabupaten Kampar)

This research was conducted in the Village of Gunung Sahilan District of Gunung Sahilan Kampar regency. The purpose of this study was to determine the contribution of honey bee beehive farm to the family income of farmers in the Village of Gunung Sahilan District of Gunung Sahilan Kampar regency. This study uses a sampling technique saturated (census) saturated sampling technique (census) is the sampling technique when the number of relatively small population, less than 30 people, in which all members of the population sampled. 27 samples were selected. The analytical method used in this research is quantitative descriptive method by describing the whole object of research with the number and percentage into the later described sentence description. The results showed that farm Honey beehive has contributed to the family income of farmers. The results showed that farm Honey beehive is the livelihood of a side which has a contribution of 75% of more than half of livelihood principal contributed by 15% as farming oil palm, rubber farming and a 10% contribution comes from donations income than farming honey beehive nonagricultural

Analisis Produksi Tanaman Karet di Desa Terbangiang Kecamatan Bandar Petalangan Kabupaten Pelalawan

This research was conducted in the Village of Terbangiang Bandar Petalangan Pelalawan. The purpose of this study was to determine the factors thatinfluence the production of rubber, how the condition of scale and efficient use of capital and labor in the rubber plant in the Village of Terbangiang Bandar Petalangan Pelalawan. In this study, the population is around the rubber farmers in the Village of Terbangiang Bandar Petalangan Pelalawan in 2013, as many as 221 families. The sampling technique used is random sampling, ie random sampling technique. Where the number of samples taken 69 samples of the population. Methods of data analysis used in this study was descriptive quantitative, where all the values of the variables obtained in the natural logarithm transformed and continued to analyze the data and simultaneous partial. Simultaneous testing (F test) showed that capital and labor jointly significantly affect the production of rubber trees in the Village of Terbangiang Bandar Petalangan Pelalawan. With the calculated F value of 19,508 and the value of F table at 3.980. Based on calculations known value of 0.512 or 51.20% R2 sebesar factors affecting the production of rubber plants are capital and labor. Rubber plant scale production effort to describe Decreasing Scale. The use of capital and labor in the production of rubber plants are not efficient

Peran Bank Rakyat Indonesia (Bri) Unit Kota Garo Terhadap Peningkatan USAhatani Kelapa Sawit Di Desa Tanah Tinggi Kecamatan Tapung Hilir Kabupaten Kampar Tahun 2014

This research is conducted in subdistrict of Tapung go downstream camphor regency. Target of this research is conducted to know role of Bank Rakyat Indonesia of unit town of garo to improvement of is effort farmer of oil palm in countryside of highlands of subdistrict of tapung go downstream regency of camphor in the year 2014in this research is methodologies used by quantitative and descriptive with program spss, where sampel used by that is farmer of oil palm borrowing fund in bri, farmer of oil palm which do not borrow fund in bri. to determine sampel use formula slovin,. Technics of data collecting through interview, observation and quetioner.from analyst result of covering clean revenue analysis data, bruto analyst data, total cost analysis, role of Bank Rakyat Indonesia unit of town of garo to improvement of earnings of farmer of oil palm that is equal to rp 117.475.400,- per 2 hectare of per year (12 month) or about rp. 12.070.000,- per month. While net earning from farmer of oil palm which do not borrow fund in bank of BRI that is equal to rp 46.118.640,- per year (12 month) or about rp 3.843.220,- per month. there are difference of net earning of per 2 hectare of per year of equal to rp 71.356.536,- or equal to rp 8.226.780,-per of month

Derivation of a dynamic model of the kinetics of nitrogen uptake throughout the growth of lettuce : calibration and validation

A kinetic model of nitrogen (N) uptake throughout growth was developed for lettuce cultivated in nutrient solution under varying natural light conditions. The model couples nitrogen uptake with dry matter accumulation using a two-compartment mechanistic approach, incorporating structural and non-structural pools. Maximum nitrogen uptake rates are assumed to decline with shoot dry weight, to allow for the effects of plant age. The model was parameterized using data from the literature, and calibrated for differences in light intensity using an optimization algorithm utilizing data from three experiments in different growing seasons. The calibrated model was validated against the data from two independent experiments conducted under different light conditions. Results showed that the model made good predictions of nitrogen uptake by plants from seedlings to maturity under fluctuating light levels in a glasshouse. Plants grown at a higher light intensity showed larger maximum nitrogen uptake rates, but the effect of light intensity declined towards plant maturity